Abstract
Linear stability theory is applied to the problem of stability of natural convection that occurs in a layer of viscoelastic liquid (Oldroyd liquid B) between two parallel vertical plates maintained at constant and different temperatures. The modified Orr-Sommerfeld equation and the thermal disturbance equation are derived without making any approximation other than the Boussinesq one. The Chebyshev collocation method is used to obtain the eigenvalue equation, which is then solved numerically with the aid of the Muller method, and the stability conditions are obtained for wide ranges of various parameters. It is found that depending upon the values of various parameters, instability sets in as either stationary or travelling-wave mode, and that elasticity has both stabilizing and destabilizing effects on the flow.
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